The Liouville operator for the CRN (REF ) in
number-potential fields is computed by standard
methods [1]} to be
\(\hat{\mathcal {L}}& =\left( 1 - e^{{\eta }_A} \right)\left(\epsilon + {\kappa }_1 x_A x_B\right) +\left( 1 - e^{- {\eta }_A} \right)\left({\kappa }_2 + {\bar{\kappa }}_1 x_A x_B\right) x_A\nonumber \\& \mbox{} +\left( 1 - e^{{\eta }_B} \right)\left(\varepsilon + {\kappa }_1 x_A x_B\right) +\left( 1 - e^{- {\eta }_B} \right)\left({\kappa }_2 + {\bar{\kappa }}_1 x_A x_B\right) x_B\) 
